The Blue Jays sent minor league left-hander Colton Turner to Chicago in Friday's waiver deal. Navarro is likely to be the backup in Toronto behind Russell Martin.
Navarro was texting with a Toronto player when White Sox general manager Rick Hahn interrupted to tell him of the trade.
"The player was asking him if he had heard anything about them possibly going after him again. When I was explaining to him he had been traded he started typing in, 'Yeah, I just heard something,''' Hahn said.
Navarro, 32, spent two seasons with the Blue Jays before signing a one-year, $4 million deal with the White Sox as a free agent in December. He has struggled this season, hitting .210 with six homers and 32 RBIs in 85 games.
Blue Jays general manager Ross Atkins said Navarro was excited by the opportunity to reunite with his former team.
"I could see the smile through the phone," Atkins said. "This should be a boost of energy for him, coming into a contender."
Toronto entered play Friday tied with Boston atop the American League East.
Atkins said Toronto's coaching staff was also pleased to hear Navarro was returning.
"They were extremely excited about, not just what he means as a catcher, but just an overall teammate," he said.
Atkins said the Blue Jays continue to explore further moves.
"At this point, you have to be really aggressive to get something done," he said. "Every day we'll look to make this team better, but there's nothing imminent."
The White Sox were looking to clear a roster spot with catcher Alex Avila set to come off the disabled list.
Turner, 25, has split time between Class A and Double-A this season, going 3-1 with a 1.33 ERA in 44 games.
"He's 94-95 (mph) on the fastball, plus slider with good command,'' Hahn said of Turner. "He's effective against both righties and lefties, so hopefully his role won't be limited to simply matching up against lefties.''